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vera_ewing

  • one year ago

Compare the functions

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  1. vera_ewing
    • one year ago
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  2. vera_ewing
    • one year ago
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    g(x) right? @freckles

  3. freckles
    • one year ago
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    let's play with it together

  4. freckles
    • one year ago
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    do you know the range of sin(x) is -1 to 1 ?

  5. vera_ewing
    • one year ago
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    Well I'm thinking 2 spots on the number line from -1 to 1. lol

  6. freckles
    • one year ago
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    so one of the following will give the min to f -3(-1)+2 -3(1)+2 so what is the min of f? notice the parabola h is in vertex form h=(x-h)^2+k where (h,k) is vertex k gives the min value of the function

  7. freckles
    • one year ago
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    and given that what is also the min of h?

  8. freckles
    • one year ago
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    the function h

  9. freckles
    • one year ago
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    sorry I should have recalled the x-coordinate of the vertex something else

  10. freckles
    • one year ago
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    h=(x-c)^2+k where (c,k) is vertex k gives the min value of this function

  11. vera_ewing
    • one year ago
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    Ohh wait I totally read the question wrong! It asks for minimum, not maximum!

  12. freckles
    • one year ago
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    yep we want the smallest possible y per function

  13. vera_ewing
    • one year ago
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    So f(x) is the greatest! Thank you :)

  14. vera_ewing
    • one year ago
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    Wait no...hold on I'm redoing it.

  15. freckles
    • one year ago
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    you didn't answer my question of the two numbers I mentioned above for f can you tell me the smallest y value

  16. freckles
    • one year ago
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    really big hint: \[-1 \le \sin(x- \pi) \le 1 \\ \text{ multiply both sides by -3 } \\ 3 \ge -3\sin(x-\pi) \ge -3 \\ \\ \text{ add 2 on both sides } 3+2 \ge -3\sin(x-\pi)+2 \ge -3+2 \]

  17. vera_ewing
    • one year ago
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    Oh they're all the same? So it's D?

  18. freckles
    • one year ago
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    yes -3+2 is the min of f and -1 is the min of g and -1 is also the min of h

  19. freckles
    • one year ago
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    -3+2=-1=-1

  20. vera_ewing
    • one year ago
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    Ohhh okay! Thank you so much! :)

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